Gradient schemes for Stokes problem

Jerome Droniou, Robert Eymard, Pierre Feron

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)

Abstract

The gradient schemes framework encompasses several conforming and nonconforming numerical schemes for diffusion equations. We develop here this framework for the approximation of the steady-state and transient incompressible Stokes equations with homogeneous Dirichlet boundary conditions. Using this framework, we establish generic convergence results - by error estimates in the case of the steady problem, and by compactness arguments in the case of the transient problem - that are applicable to both old and new schemes for Stokes' equations. Three classical methods (MAC, Taylor-Hood and Crouzeix-Raviart schemes) are shown to fit into the gradient schemes framework; some of the convergence results obtained for those through the framework are new. We also show that a Hybrid Mimetic Mixed scheme, extension of the Crouzeix-Raviart scheme to a very general polyhedral mesh, can be designed within the gradient schemes framework; this scheme is new for Stokes' equations, and our abstract analysis establishes its convergence along with error estimates.

Original languageEnglish
Pages (from-to)1636-1669
Number of pages34
JournalIMA Journal of Numerical Analysis
Volume36
Issue number4
DOIs
Publication statusPublished - 1 Oct 2016

Keywords

  • convergence study
  • error estimate
  • gradient schemes
  • stokes equation

Cite this

Droniou, Jerome ; Eymard, Robert ; Feron, Pierre. / Gradient schemes for Stokes problem. In: IMA Journal of Numerical Analysis. 2016 ; Vol. 36, No. 4. pp. 1636-1669.
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Gradient schemes for Stokes problem. / Droniou, Jerome; Eymard, Robert; Feron, Pierre.

In: IMA Journal of Numerical Analysis, Vol. 36, No. 4, 01.10.2016, p. 1636-1669.

Research output: Contribution to journalArticleResearchpeer-review

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